Numerical weather predicting models often require solving a 3-D Helmholtz problem which derived from the governing equation of dynamical core in Met Office Unified Model, by preconditioned iterative solvers. In this dissertation, a GPU implementation of preconditioned conjugate gradient (CG) iterative method will be focused on. A given serial code has been ported on GPU. According to the porting, performance analysis and optimisation will be carried out. At last, this dissertation defines the main performance bottleneck of the GPU implementation of preconditioned CG. According to these analyses, an initial optimisation and further optimisation suggestions will be shown in this dissertation.